for Journals by Title or ISSN
for Articles by Keywords
help
  Subjects -> ENGINEERING (Total: 2255 journals)
    - CHEMICAL ENGINEERING (189 journals)
    - CIVIL ENGINEERING (180 journals)
    - ELECTRICAL ENGINEERING (99 journals)
    - ENGINEERING (1196 journals)
    - ENGINEERING MECHANICS AND MATERIALS (386 journals)
    - HYDRAULIC ENGINEERING (55 journals)
    - INDUSTRIAL ENGINEERING (61 journals)
    - MECHANICAL ENGINEERING (89 journals)

ENGINEERING (1196 journals)

The end of the list has been reached or no journals were found for your choice.
Journal Cover Physica D: Nonlinear Phenomena
  [SJR: 1.049]   [H-I: 102]   [3 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0167-2789
   Published by Elsevier Homepage  [3039 journals]
  • A theory of synchrony by coupling through a diffusive chemical signal
    • Authors: Jia Gou; Wei-Yin Chiang; Pik-Yin Lai; Michael J. Ward; Yue-Xian Li
      Pages: 1 - 17
      Abstract: Publication date: 15 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 339
      Author(s): Jia Gou, Wei-Yin Chiang, Pik-Yin Lai, Michael J. Ward, Yue-Xian Li
      We formulate and analyze oscillatory dynamics associated with a model of dynamically active, but spatially segregated, compartments that are coupled through a chemical signal that diffuses in the bulk medium between the compartments. The coupling between each compartment and the bulk is due to both feedback terms to the compartmental dynamics and flux boundary conditions at the interface between the compartment and the bulk. Our coupled model consists of dynamically active compartments located at the two ends of a 1-D bulk region of spatial extent 2 L . The dynamics in the two compartments is modeled by Sel’kov kinetics, and the signaling molecule between the two-compartments is assumed to undergo both diffusion, with diffusivity D , and first-order, linear, bulk degradation. For the resulting PDE–ODE system, we construct a symmetric steady-state solution and analyze the stability of this solution to either in-phase synchronous or anti-phase synchronous perturbations about the midline x = L . The conditions for the onset of oscillatory dynamics, as obtained from a linearization of the steady-state solution, are studied using a winding number approach. Global branches of either in-phase or anti-phase periodic solutions, and their associated stability properties, are determined numerically. For the case of a linear coupling between the compartments and the bulk, with coupling strength β , a phase diagram, in the parameter space D versus β is constructed that shows the existence of a rather wide parameter regime where stable in-phase synchronized oscillations can occur between the two compartments. By using a Floquet-based approach, this analysis with linear coupling is then extended to determine Hopf bifurcation thresholds for a periodic chain of evenly-spaced dynamically active units. Finally, we consider one particular case of a nonlinear coupling between two active compartments and the bulk. It is shown that stable in-phase and anti-phase synchronous oscillations also occur in certain parameter regimes, but as isolated solution branches that are disconnected from the steady-state solution branch.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.08.004
      Issue No: Vol. 339 (2016)
       
  • Global dynamics for steep nonlinearities in two dimensions
    • Authors: Tomáš Gedeon; Shaun Harker; Hiroshi Kokubu; Konstantin Mischaikow; Hiroe Oka
      Pages: 18 - 38
      Abstract: Publication date: 15 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 339
      Author(s): Tomáš Gedeon, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka
      This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we associate a Morse graph, a computable object that describes a Morse decomposition of the dynamics. In this paper we show that all smooth perturbations of the switching system share the same Morse graph and we compute explicit bounds on the size of the allowable perturbation. This shows that computationally tractable switching systems can be used to characterize dynamics of smooth systems with steep nonlinearities.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.08.006
      Issue No: Vol. 339 (2016)
       
  • Analysis of the Poisson–Nernst–Planck equation in a ball for modeling
           the Voltage–Current relation in neurobiological microdomains
    • Authors: J. Cartailler; Z. Schuss; D. Holcman
      Pages: 39 - 48
      Abstract: Publication date: 15 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 339
      Author(s): J. Cartailler, Z. Schuss, D. Holcman
      The electro-diffusion of ions is often described by the Poisson–Nernst–Planck (PNP) equations, which couple nonlinearly the charge concentration and the electric potential. This model is used, among others, to describe the motion of ions in neuronal micro-compartments. It remains at this time an open question how to determine the relaxation and the steady state distribution of voltage when an initial charge of ions is injected into a domain bounded by an impermeable dielectric membrane. The purpose of this paper is to construct an asymptotic approximation to the solution of the stationary PNP equations in a d -dimensional ball ( d = 1 , 2 , 3 ) in the limit of large total charge. In this geometry the PNP system reduces to the Liouville–Gelfand–Bratú (LGB) equation, with the difference that the boundary condition is Neumann, not Dirichlet, and there is a minus sign in the exponent of the exponential term. The entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson’s equation. These differences replace attraction by repulsion in the LGB equation, thus completely changing the solution. We find that the voltage is maximal in the center and decreases toward the boundary. We also find that the potential drop between the center and the surface increases logarithmically in the total number of charges and not linearly, as in classical capacitance theory. This logarithmic singularity is obtained for d = 3 from an asymptotic argument and cannot be derived from the analysis of the phase portrait. These results are used to derive the relation between the outward current and the voltage in a dendritic spine, which is idealized as a dielectric sphere connected smoothly to the nerve axon by a narrow neck. This is a fundamental microdomain involved in neuronal communication. We compute the escape rate of an ion from the steady density in a ball, which models a neuronal spine head, to a small absorbing window in the sphere. We predict that the current is defined by the narrow neck that is connected to the sphere by a small absorbing window, as suggested by the narrow escape theory, while voltage is controlled by the PNP equations independently of the neck.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.09.001
      Issue No: Vol. 339 (2016)
       
  • Numerical analysis of the rescaling method for parabolic problems with
           blow-up in finite time
    • Authors: V.T. Nguyen
      Pages: 49 - 65
      Abstract: Publication date: 15 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 339
      Author(s): V.T. Nguyen
      In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation u ↦ u λ ( x , t ) : = λ 2 p − 1 u ( λ x , λ 2 t ) . For that purpose, we apply the rescaling method proposed by Berger and Kohn (1988) to such problems. The convergence of the method is proved under some regularity assumption. Some numerical experiments are given to derive the blow-up profile verifying henceforth the theoretical results.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.09.002
      Issue No: Vol. 339 (2016)
       
  • A Hierarchical Bayes Ensemble Kalman Filter
    • Authors: Michael Tsyrulnikov; Alexander Rakitko
      Pages: 1 - 16
      Abstract: Publication date: 1 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 338
      Author(s): Michael Tsyrulnikov, Alexander Rakitko
      A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of “truth”. The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filters.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.07.009
      Issue No: Vol. 338 (2016)
       
  • The tennis racket effect in a three-dimensional rigid body
    • Authors: Léo Van Damme; Pavao Mardešić; Dominique Sugny
      Pages: 17 - 25
      Abstract: Publication date: 1 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 338
      Author(s): Léo Van Damme, Pavao Mardešić, Dominique Sugny
      We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ( π - rotation) of the head of the racket when a full ( 2 π ) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.07.010
      Issue No: Vol. 338 (2016)
       
  • Stability analysis of amplitude death in delay-coupled high-dimensional
           map networks and their design procedure
    • Authors: Tomohiko Watanabe; Yoshiki Sugitani; Keiji Konishi; Naoyuki Hara
      Pages: 26 - 33
      Abstract: Publication date: 1 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 338
      Author(s): Tomohiko Watanabe, Yoshiki Sugitani, Keiji Konishi, Naoyuki Hara
      The present paper studies amplitude death in high-dimensional maps coupled by time-delay connections. A linear stability analysis provides several sufficient conditions for an amplitude death state to be unstable, i.e., an odd number property and its extended properties. Furthermore, necessary conditions for stability are provided. These conditions, which reduce trial-and-error tasks for design, and the convex direction, which is a popular concept in the field of robust control, allow us to propose a design procedure for system parameters, such as coupling strength, connection delay, and input–output matrices, for a given network topology. These analytical results are confirmed numerically using delayed logistic maps, generalized Henon maps, and piecewise linear maps.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.07.011
      Issue No: Vol. 338 (2016)
       
  • Generalized uncertainty principle and analogue of quantum gravity in
           optics
    • Authors: Maria Chiara Braidotti; Ziad H. Musslimani; Claudio Conti
      Pages: 34 - 41
      Abstract: Publication date: 1 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 338
      Author(s): Maria Chiara Braidotti, Ziad H. Musslimani, Claudio Conti
      The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while implementing sub-wavelength optical schemes is how to overcome the limitations set by standard Fourier optics. A strategy to overcome these difficulties is to utilize the concept of a generalized uncertainty principle (G-UP) which has been originally developed to study quantum gravity. In this paper we propose to use the concept of G-UP within the framework of optics to show that the generalized Schrödinger equation describing short pulses and ultra-focused beams predicts the existence of a minimal spatial or temporal scale which in turn implies the existence of maximally localized states. Using a Gaussian wavepacket with complex phase, we derive the corresponding generalized uncertainty relation and its maximally localized states. Furthermore, we numerically show that the presence of nonlinearity helps the system to reach its maximal localization. Our results may trigger further theoretical and experimental tests for practical applications and analogues of fundamental physical theories.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.08.001
      Issue No: Vol. 338 (2016)
       
  • Initial–boundary layer associated with the nonlinear
           Darcy–Brinkman–Oberbeck–Boussinesq system
    • Authors: Mingwen Fei; Daozhi Han; Xiaoming Wang
      Pages: 42 - 56
      Abstract: Publication date: 1 January 2017
      Source:Physica D: Nonlinear Phenomena, Volume 338
      Author(s): Mingwen Fei, Daozhi Han, Xiaoming Wang
      In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial–boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.08.002
      Issue No: Vol. 338 (2016)
       
  • Two-dimensional localized structures in harmonically forced oscillatory
           systems
    • Authors: Y.-P. Ma; E. Knobloch
      Pages: 1 - 17
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): Y.-P. Ma, E. Knobloch
      Two-dimensional spatially localized structures in the complex Ginzburg–Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on one of them. The bifurcation structures of steady circular fronts and localized target patterns are computed in the Turing-stable and Turing-unstable regimes. In particular, localized target patterns grow along the solution branch via ring insertion at the core in a process reminiscent of defect-mediated snaking in one spatial dimension. Stability of axisymmetric solutions on these branches with respect to axisymmetric and nonaxisymmetric perturbations is determined, and parameter regimes with stable axisymmetric oscillons are identified. Direct numerical simulations reveal novel depinning dynamics of localized target patterns in the radial direction, and of circular and planar localized hexagonal patterns in the fully two-dimensional system.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.003
      Issue No: Vol. 337 (2016)
       
  • A comparison of macroscopic models describing the collective response of
           sedimenting rod-like particles in shear flows
    • Authors: Christiane Helzel; Athanasios E. Tzavaras
      Pages: 18 - 29
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): Christiane Helzel, Athanasios E. Tzavaras
      We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity, presented in Helzel and Tzavaras (submitted for publication). Here we restrict our considerations to shear flow and consider a simplified situation, where the particle orientation is restricted to the plane spanned by the direction of shear and the direction of gravity. For this simplified kinetic model we carry out a linear stability analysis and we derive two different nonlinear macroscopic models which describe the formation of clusters of higher particle density. One of these macroscopic models is based on a diffusive scaling, the other one is based on a so-called quasi-dynamic approximation. Numerical computations, which compare the predictions of the macroscopic models with the kinetic model, complete our presentation.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.004
      Issue No: Vol. 337 (2016)
       
  • Exploiting stiffness nonlinearities to improve flow energy capture from
           the wake of a bluff body
    • Authors: Ali H. Alhadidi; Hamid Abderrahmane; Mohammed F. Daqaq
      Pages: 30 - 42
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): Ali H. Alhadidi, Hamid Abderrahmane, Mohammed F. Daqaq
      Fluid–structure coupling mechanisms such as wake galloping have been recently utilized to develop scalable flow energy harvesters. Unlike traditional rotary-type generators which are known to suffer serious scalability issues because their efficiency drops significantly as their size decreases; wake-galloping flow energy harvesters (FEHs) operate using a very simple motion mechanism, and, hence can be scaled down to fit the desired application. Nevertheless, wake-galloping FEHs have their own shortcomings. Typically, a wake-galloping FEH has a linear restoring force which results in a very narrow lock-in region. As a result, it does not perform well under the broad range of shedding frequencies normally associated with a variable flow speed. To overcome this critical problem, this article demonstrates theoretically and experimentally that, a bi-stable restoring force can be used to broaden the steady-state bandwidth of wake galloping FEHs and, thereby to decrease their sensitivity to variations in the flow speed. An experimental case study is carried out in a wind tunnel to compare the performance of a bi-stable and a linear FEH under single- and multi-frequency vortex street. An experimentally-validated lumped-parameters model of the bi-stable harvester is also introduced, and solved using the method of multiple scales to study the influence of the shape of the potential energy function on the output voltage.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.005
      Issue No: Vol. 337 (2016)
       
  • Variety of strange pseudohyperbolic attractors in three-dimensional
           generalized Hénon maps
    • Authors: A.S. Gonchenko; S.V. Gonchenko
      Pages: 43 - 57
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): A.S. Gonchenko, S.V. Gonchenko
      In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attractors in that sense that each orbit in the attractor has positive maximal Lyapunov exponent and this property is robust, i.e., it holds for all close systems. We restrict attention to the study of pseudohyperbolic attractors that contain only one fixed point. Then we show that three-dimensional maps may have only 5 different types of such attractors, which we call the discrete Lorenz, figure-8, double-figure-8, super-figure-8, and super-Lorenz attractors. We find the first four types of attractors in three-dimensional generalized Hénon maps of form x ̄ = y , y ̄ = z , z ̄ = B x + A z + C y + g ( y , z ) , where A , B and C are parameters ( B is the Jacobian) and g ( 0 , 0 ) = g ′ ( 0 , 0 ) = 0 .

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.006
      Issue No: Vol. 337 (2016)
       
  • Oscillatory instabilities of gap solitons in a repulsive
           Bose–Einstein condensate
    • Authors: P.P. Kizin; D.A. Zezyulin; G.L. Alfimov
      Pages: 58 - 66
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): P.P. Kizin, D.A. Zezyulin, G.L. Alfimov
      The paper is devoted to numerical study of stability of nonlinear localized modes (“gap solitons”) for the spatially one-dimensional Gross–Pitaevskii equation (1D GPE) with periodic potential and repulsive interparticle interactions. We use the Evans function approach combined with the exterior algebra formulation in order to detect and describe weak oscillatory instabilities. We show that the simplest (“fundamental”) gap solitons in the first and in the second spectral gap undergo oscillatory instabilities for certain values of the frequency parameter (i.e., the chemical potential). The number of unstable eigenvalues and the associated instability rates are described. Several stable and unstable more complex (non-fundamental) gap solitons are also discussed. The results obtained from the Evans function approach are independently confirmed using the direct numerical integration of the GPE.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.007
      Issue No: Vol. 337 (2016)
       
  • Limit cycles in planar piecewise linear differential systems with
           nonregular separation line
    • Authors: Pedro Toniol Cardin; Joan Torregrosa
      Pages: 67 - 82
      Abstract: Publication date: 15 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 337
      Author(s): Pedro Toniol Cardin, Joan Torregrosa
      In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2 π − α , respectively, for α ∈ ( 0 , π ) . We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α , we prove the existence of systems with four limit cycles up to fifth order and, for α = π / 2 , we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.07.008
      Issue No: Vol. 337 (2016)
       
  • Causal hydrodynamics from kinetic theory by doublet scheme in
           renormalization-group method
    • Authors: Kyosuke Tsumura; Yuta Kikuchi; Teiji Kunihiro
      Pages: 1 - 27
      Abstract: Publication date: 1 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 336
      Author(s): Kyosuke Tsumura, Yuta Kikuchi, Teiji Kunihiro
      We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by zero modes. We call this framework the doublet scheme. The validity of the doublet scheme is first tested and demonstrated by taking the Lorenz model as a simple three-dimensional dynamical system; it is shown that the two-dimensional reduced dynamics on the attractive manifold composed of the would-be zero and a fast modes are successfully obtained in a natural way. We then apply the doublet scheme to construct causal hydrodynamics as a mesoscopic dynamics of kinetic theory, i.e., the Boltzmann equation, in a systematic manner with no ad-hoc assumption. It is found that our equation has the same form as Grad’s thirteen-moment causal hydrodynamic equation, but the microscopic formulae of the transport coefficients and relaxation times are different. In fact, in contrast to the Grad equation, our equation leads to the same expressions for the transport coefficients as given by the Chapman–Enskog expansion method and suggests novel formulae of the relaxation times expressed in terms of relaxation functions which allow a natural physical interpretation of the relaxation times. Furthermore, our theory nicely gives the explicit forms of the distribution function and the thirteen hydrodynamic variables in terms of the linearized collision operator, which in turn clearly suggest the proper ansatz forms of them to be adopted in the method of moments.

      PubDate: 2016-10-16T12:47:09Z
      DOI: 10.1016/j.physd.2016.06.012
      Issue No: Vol. 336 (2016)
       
  • Towards the modeling of nanoindentation of virus shells: Do substrate
           adhesion and geometry matter?
    • Authors: Arthur Bousquet; Bogdan Dragnea; Manel Tayachi; Roger Temam
      Pages: 28 - 38
      Abstract: Publication date: 1 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 336
      Author(s): Arthur Bousquet, Bogdan Dragnea, Manel Tayachi, Roger Temam
      Soft nanoparticles adsorbing at surfaces undergo deformation and buildup of elastic strain as a consequence of interfacial adhesion of similar magnitude with constitutive interactions. An example is the adsorption of virus particles at surfaces, a phenomenon of central importance for experiments in virus nanoindentation and for understanding of virus entry. The influence of adhesion forces and substrate corrugation on the mechanical response to indentation has not been studied. This is somewhat surprising considering that many single-stranded RNA icosahedral viruses are organized by soft intermolecular interactions while relatively strong adhesion forces are required for virus immobilization for nanoindentation. This article presents numerical simulations via finite elements discretization investigating the deformation of a thick shell in the context of slow evolution linear elasticity and in presence of adhesion interactions with the substrate. We study the influence of the adhesion forces in the deformation of the virus model under axial compression on a flat substrate by comparing the force–displacement curves for a shell having elastic constants relevant to virus capsids with and without adhesion forces derived from the Lennard-Jones potential. Finally, we study the influence of the geometry of the substrate in two-dimensions by comparing deformation of the virus model adsorbed at the cusp between two cylinders with that on a flat surface.

      PubDate: 2016-10-16T12:47:09Z
      DOI: 10.1016/j.physd.2016.06.013
      Issue No: Vol. 336 (2016)
       
  • Fluctuations induced transition of localization of granular objects caused
           by degrees of crowding
    • Authors: Soutaro Oda; Yoshitsugu Kubo; Chwen-Yang Shew; Kenichi Yoshikawa
      Pages: 39 - 46
      Abstract: Publication date: 1 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 336
      Author(s): Soutaro Oda, Yoshitsugu Kubo, Chwen-Yang Shew, Kenichi Yoshikawa
      Fluctuations are ubiquitous in both microscopic and macroscopic systems, and an investigation of confined particles under fluctuations is relevant to how living cells on the earth maintain their lives. Inspired by biological cells, we conduct the experiment through a very simple fluctuating system containing one or several large spherical granular particles and multiple smaller ones confined on a cylindrical dish under vertical vibration. We find a universal behavior that large particles preferentially locate in cavity interior due to the fact that large particles are depleted from the cavity wall by small spheres under vertical vibration in the actual experiment. This universal behavior can be understood from the standpoint of entropy.

      PubDate: 2016-10-16T12:47:09Z
      DOI: 10.1016/j.physd.2016.06.014
      Issue No: Vol. 336 (2016)
       
  • Coupled oscillators on evolving networks
    • Authors: R.K. Singh; Trilochan Bagarti
      Pages: 47 - 52
      Abstract: Publication date: 1 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 336
      Author(s): R.K. Singh, Trilochan Bagarti
      In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.

      PubDate: 2016-10-16T12:47:09Z
      DOI: 10.1016/j.physd.2016.06.015
      Issue No: Vol. 336 (2016)
       
  • Emergence of chaos in a spatially confined reactive system
    • Authors: Valérie Voorsluijs; Yannick De Decker
      Pages: 1 - 9
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Valérie Voorsluijs, Yannick De Decker
      In spatially restricted media, interactions between particles and local fluctuations of density can lead to important deviations of the dynamics from the unconfined, deterministic picture. In this context, we investigated how molecular crowding can affect the emergence of chaos in small reactive systems. We developed to this end an amended version of the Willamowski–Rössler model, where we account for the impenetrability of the reactive species. We analyzed the deterministic kinetics of this model and studied it with spatially-extended stochastic simulations in which the mobility of particles is included explicitly. We show that homogeneous fluctuations can lead to a destruction of chaos through a fluctuation-induced collision between chaotic trajectories and absorbing states. However, an interplay between the size of the system and the mobility of particles can counterbalance this effect so that chaos can indeed be found when particles diffuse slowly. This unexpected effect can be traced back to the emergence of spatial correlations which strongly affect the dynamics. The mobility of particles effectively acts as a new bifurcation parameter, enabling the system to switch from stationary states to absorbing states, oscillations or chaos.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.05.005
      Issue No: Vol. 335 (2016)
       
  • Breather solutions for inhomogeneous FPU models using Birkhoff normal
           forms
    • Authors: Francisco Martínez-Farías; Panayotis Panayotaros
      Pages: 10 - 25
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Francisco Martínez-Farías, Panayotis Panayotaros
      We present results on spatially localized oscillations in some inhomogeneous nonlinear lattices of Fermi–Pasta–Ulam (FPU) type derived from phenomenological nonlinear elastic network models proposed to study localized protein vibrations. The main feature of the FPU lattices we consider is that the number of interacting neighbors varies from site to site, and we see numerically that this spatial inhomogeneity leads to spatially localized normal modes in the linearized problem. This property is seen in 1-D models, and in a 3-D model with a geometry obtained from protein data. The spectral analysis of these examples suggests some non-resonance assumptions that we use to show the existence of invariant subspaces of spatially localized solutions in quartic Birkhoff normal forms of the FPU systems. The invariant subspaces have an additional symmetry and this fact allows us to compute periodic orbits of the quartic normal form in a relatively simple way.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.06.004
      Issue No: Vol. 335 (2016)
       
  • Kinetic theory of cluster dynamics
    • Authors: Robert I.A. Patterson; Sergio Simonella; Wolfgang Wagner
      Pages: 26 - 32
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Robert I.A. Patterson, Sergio Simonella, Wolfgang Wagner
      In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, defined as finite groups of particles having an influence on each other’s trajectory during a given interval of time. For an ideal gas with short-range intermolecular force, we provide a description of the cluster size distribution in terms of the reduced Boltzmann density. In the simplified context of Maxwell molecules, we show that a macroscopic fraction of the gas forms a giant component in finite kinetic time. The critical index of this phase transition is in agreement with previous numerical results on the elastic billiard.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.06.007
      Issue No: Vol. 335 (2016)
       
  • Frequency locking near the gluing bifurcation: Spin-torque oscillator
           under periodic modulation of current
    • Authors: Michael A. Zaks; Arkady Pikovsky
      Pages: 33 - 44
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Michael A. Zaks, Arkady Pikovsky
      We consider entrainment by periodic force of limit cycles which are close to the homoclinic bifurcation. Taking as a physical example the nanoscale spin-torque oscillator in the LC circuit, we develop the general description of the situation in which the frequency of the stable periodic orbit in the autonomous system is highly sensitive to minor variations of the parameter, and derive explicit expressions for the strongly deformed borders of the resonance regions (Arnold tongues) in the parameter space of the problem. It turns out that proximity to homoclinic bifurcations hinders synchronization of spin-torque oscillators.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.06.008
      Issue No: Vol. 335 (2016)
       
  • Chaotic sub-dynamics in coupled logistic maps
    • Authors: Marek Lampart; Piotr Oprocha
      Pages: 45 - 53
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Marek Lampart, Piotr Oprocha
      We study the dynamics of Laplacian-type coupling induced by logistic family f μ ( x ) = μ x ( 1 − x ) , where μ ∈ [ 0 , 4 ] , on a periodic lattice, that is the dynamics of maps of the form F ( x , y ) = ( ( 1 − ε ) f μ ( x ) + ε f μ ( y ) , ( 1 − ε ) f μ ( y ) + ε f μ ( x ) ) where ε > 0 determines strength of coupling. Our main objective is to analyze the structure of attractors in such systems and especially detect invariant regions with nontrivial dynamics outside the diagonal. In analytical way, we detect some regions of parameters for which a horseshoe is present; and using simulations global attractors and invariant sets are depicted.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.06.010
      Issue No: Vol. 335 (2016)
       
  • A hierarchy of Poisson brackets in non-equilibrium thermodynamics
    • Authors: Michal Pavelka; Václav Klika; Oğul Esen; Miroslav Grmela
      Pages: 54 - 69
      Abstract: Publication date: 15 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 335
      Author(s): Michal Pavelka, Václav Klika, Oğul Esen, Miroslav Grmela
      Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed and what additional features we also gain by the construction. In particular, the Poisson brackets governing reversible evolution in one-particle kinetic theory, kinetic theory of binary mixtures, binary fluid mixtures, classical irreversible thermodynamics and classical hydrodynamics are derived from Liouville equation. Although the construction is quite natural, a few examples where it does not work are included (e.g. the BBGKY hierarchy). Finally, a new infinite grand-canonical hierarchy of Poisson brackets is proposed, which leads to Poisson brackets expressing non-local phenomena such as turbulent motion or evolution of polymeric fluids. Eventually, Lie–Poisson structures standing behind some of the brackets are identified.

      PubDate: 2016-10-02T03:34:48Z
      DOI: 10.1016/j.physd.2016.06.011
      Issue No: Vol. 335 (2016)
       
  • Topology in Dynamics, Differential Equations, and Data
    • Authors: Sarah Day; Robertus C.A.M. Vandervorst; Thomas Wanner
      Pages: 1 - 3
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Sarah Day, Robertus C.A.M. Vandervorst, Thomas Wanner
      This special issue is devoted to showcasing recent uses of topological methods in the study of dynamical behavior and the analysis of both numerical and experimental data. The twelve original research papers span a wide spectrum of results from abstract index theories, over homology- and persistence-based data analysis techniques, to computer-assisted proof techniques based on topological fixed point arguments.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.08.003
      Issue No: Vol. 334 (2016)
       
  • Geometric phase in the Hopf bundle and the stability of non-linear waves
    • Authors: Colin J. Grudzien; Thomas J. Bridges; Christopher K.R.T. Jones
      Pages: 4 - 18
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Colin J. Grudzien, Thomas J. Bridges, Christopher K.R.T. Jones
      We develop a stability index for the traveling waves of non-linear reaction–diffusion equations using the geometric phase induced on the Hopf bundle S 2 n − 1 ⊂ C n . This can be viewed as an alternative formulation of the winding number calculation of the Evans function, whose zeros correspond to the eigenvalues of the linearization of reaction–diffusion operators about the wave. The stability of a traveling wave can be determined by the existence of eigenvalues of positive real part for the linear operator. Our method of geometric phase for locating and counting eigenvalues is inspired by the numerical results in Way’s Dynamics in the Hopf bundle, the geometric phase and implications for dynamical systems Way (2009). We provide a detailed proof of the relationship between the phase and eigenvalues for dynamical systems defined on C 2 and sketch the proof of the method of geometric phase for C n and its generalization to boundary-value problems. Implementing the numerical method, modified from Way (2009), we conclude with open questions inspired from the results.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.04.005
      Issue No: Vol. 334 (2016)
       
  • The Poincaré–Bendixson Theorem and the non-linear
           Cauchy–Riemann equations
    • Authors: J.B. van den Berg; S. Munaò; R.C.A.M. Vandervorst
      Pages: 19 - 28
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): J.B. van den Berg, S. Munaò, R.C.A.M. Vandervorst
      Fiedler and Mallet-Paret (1989) prove a version of the classical Poincaré–Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy–Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapunov function.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.04.009
      Issue No: Vol. 334 (2016)
       
  • Arnold’s mechanism of diffusion in the spatial circular restricted
           three-body problem: A semi-analytical argument
    • Authors: Amadeu Delshams; Marian Gidea; Pablo Roldan
      Pages: 29 - 48
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Amadeu Delshams, Marian Gidea, Pablo Roldan
      We consider the spatial circular restricted three-body problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3-degree of freedom Hamiltonian system. We fix an energy level close to that of the collinear libration point L 1 , located between Sun and Earth. Near L 1 there exists a normally hyperbolic invariant manifold, diffeomorphic to a 3-sphere. For an orbit confined to this 3-sphere, the amplitude of the motion relative to the ecliptic (the plane of the orbits of Sun and Earth) can vary only slightly. We show that we can obtain new orbits whose amplitude of motion relative to the ecliptic changes significantly, by following orbits of the flow restricted to the 3-sphere alternatively with homoclinic orbits that turn around the Earth. We provide an abstract theorem for the existence of such ‘diffusing’ orbits, and numerical evidence that the premises of the theorem are satisfied in the three-body problem considered here. We provide an explicit construction of diffusing orbits. The geometric mechanism underlying this construction is reminiscent of the Arnold diffusion problem for Hamiltonian systems. Our argument, however, does not involve transition chains of tori as in the classical example of Arnold. We exploit mostly the ‘outer dynamics’ along homoclinic orbits, and use very little information on the ‘inner dynamics’ restricted to the 3-sphere. As a possible application to astrodynamics, diffusing orbits as above can be used to design low cost maneuvers to change the inclination of an orbit of a satellite near L 1 from a nearly-planar orbit to a tilted orbit with respect to the ecliptic. We explore different energy levels, and estimate the largest orbital inclination that can be achieved through our construction.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.06.005
      Issue No: Vol. 334 (2016)
       
  • Exploring the topology of dynamical reconstructions
    • Authors: Joshua Garland; Elizabeth Bradley; James D. Meiss
      Pages: 49 - 59
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Joshua Garland, Elizabeth Bradley, James D. Meiss
      Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a number of free parameters and the computation of homology for a large number of simplices can be expensive. This paper is a study of how to compute the homology efficiently and effectively without a full (diffeomorphic) reconstruction. Using trajectories from the classic Lorenz system, we reconstruct the dynamics using the method of delays, then build a simplicial complex whose vertices are a small subset of the data: the “witness complex”. Surprisingly, we find that the witness complex correctly resolves the homology of the underlying invariant set from noisy samples of that set even if the reconstruction dimension is well below the thresholds for assuring topological conjugacy between the true and reconstructed dynamics that are specified in the embedding theorems. We conjecture that this is because the requirements for reconstructing homology are less stringent: a homeomorphism is sufficient—as opposed to a diffeomorphism, as is necessary for the full dynamics. We provide preliminary evidence that a homeomorphism, in the form of a delay-coordinate reconstruction map, may exist at a lower dimension than that required to achieve an embedding.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.03.006
      Issue No: Vol. 334 (2016)
       
  • Topological microstructure analysis using persistence landscapes
    • Authors: Paweł Dłotko; Thomas Wanner
      Pages: 60 - 81
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Paweł Dłotko, Thomas Wanner
      Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures have been proposed, which measure essential connectivity information and are based on techniques from algebraic topology. Such metrics are inherently computable using computational homology, provided the microstructures are discretized using a thresholding process. However, while in many cases the thresholding is straightforward, noise and measurement errors can lead to misleading metric values. In such situations, persistence landscapes have been proposed as a natural topology metric. Common to all of these approaches is the enormous data reduction, which passes from complicated patterns to discrete information. It is therefore natural to wonder what type of information is actually retained by the topology. In the present paper, we demonstrate that averaged persistence landscapes can be used to recover central system information in the Cahn–Hilliard theory of phase separation. More precisely, we show that topological information of evolving microstructures alone suffices to accurately detect both concentration information and the actual decomposition stage of a data snapshot. Considering that persistent homology only measures discrete connectivity information, regardless of the size of the topological features, these results indicate that the system parameters in a phase separation process affect the topology considerably more than anticipated. We believe that the methods discussed in this paper could provide a valuable tool for relating experimental data to model simulations.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.04.015
      Issue No: Vol. 334 (2016)
       
  • Analysis of Kolmogorov flow and Rayleigh–Bénard convection
           using persistent homology
    • Authors: Miroslav Kramár; Rachel Levanger; Jeffrey Tithof; Balachandra Suri; Mu Xu; Mark Paul; Michael F. Schatz; Konstantin Mischaikow
      Pages: 82 - 98
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Miroslav Kramár, Rachel Levanger, Jeffrey Tithof, Balachandra Suri, Mu Xu, Mark Paul, Michael F. Schatz, Konstantin Mischaikow
      We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium. In particular, we analyze image time series of flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh–Bénard convection. For each image we compute a persistence diagram to yield a reduced description of the flow field; by applying different metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding flow patterns. We also examine the dynamics of the flow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an effective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.02.003
      Issue No: Vol. 334 (2016)
       
  • Principal component analysis of persistent homology rank functions with
           case studies of spatial point patterns, sphere packing and colloids
    • Authors: Vanessa Robins; Katharine Turner
      Pages: 99 - 117
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Vanessa Robins, Katharine Turner
      Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functions. For a point pattern X we construct a filtration of spaces by taking the union of balls of radius a centred on points in X , X a = ∪ x ∈ X B ( x , a ) . The rank function β k ( X ) : { ( a , b ) ∈ R 2 : a ≤ b } → R is then defined by β k ( X ) ( a , b ) = rank ( ι ∗ : H k ( X a ) → H k ( X b ) ) where ι ∗ is the induced map on homology from the inclusion map on spaces. We consider the rank functions as lying in a Hilbert space and show that under reasonable conditions the rank functions from multiple simulations or experiments will lie in an affine subspace. This enables us to perform functional principal component analysis which we apply to experimental data from colloids at different effective temperatures and to sphere packings with different volume fractions. We also investigate the potential of rank functions in providing a test of complete spatial randomness of 2D point patterns using the distances to an empirically computed mean rank function of binomial point patterns in the unit square.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.03.007
      Issue No: Vol. 334 (2016)
       
  • Continuation of point clouds via persistence diagrams
    • Authors: Marcio Gameiro; Yasuaki Hiraoka; Ippei Obayashi
      Pages: 118 - 132
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi
      In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton–Raphson continuation method in this setting. Given an original point cloud P , its persistence diagram D , and a target persistence diagram D ′ , we gradually move from D to D ′ , by successively computing intermediate point clouds until we finally find a point cloud P ′ having D ′ as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2015.11.011
      Issue No: Vol. 334 (2016)
       
  • Chaos near a resonant inclination-flip
    • Authors: Marcus Fontaine; William Kalies; Vincent Naudot
      Pages: 141 - 157
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Marcus Fontaine, William Kalies, Vincent Naudot
      Horseshoes play a central role in dynamical systems and are observed in many chaotic systems. However most points in a neighborhood of the horseshoe escape after finitely many iterations. In this work we construct a new model by re-injecting the points that escape the horseshoe. We show that this model can be realized within an attractor of a flow arising from a three-dimensional vector field, after perturbation of an inclination-flip homoclinic orbit with a resonance. The dynamics of this model, without considering the re-injection, often contains a cuspidal horseshoe with positive entropy, and we show that for a computational example the dynamics with re-injection can have more complexity than the cuspidal horseshoe alone.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.06.009
      Issue No: Vol. 334 (2016)
       
  • Rigorous numerics for NLS: Bound states, spectra, and controllability
    • Authors: Roberto Castelli; Holger Teismann
      Pages: 158 - 173
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Roberto Castelli, Holger Teismann
      In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound-state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof (Beauchard et al., 2015) of the local exact controllability of NLS.

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.01.005
      Issue No: Vol. 334 (2016)
       
  • Automatic differentiation for Fourier series and the radii polynomial
           approach
    • Authors: Jean-Philippe Lessard; J.D. Mireles James; Julian Ransford
      Pages: 174 - 186
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Jean-Philippe Lessard, J.D. Mireles James, Julian Ransford
      In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

      PubDate: 2016-09-13T04:50:37Z
      DOI: 10.1016/j.physd.2016.02.007
      Issue No: Vol. 334 (2016)
       
  • Excitability, mixed-mode oscillations and transition to chaos in a
           stochastic ice ages model
    • Authors: D.V. Alexandrov; I.A. Bashkirtseva; L.B. Ryashko
      Abstract: Publication date: Available online 30 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko
      Motivated by an important geophysical significance, we consider the influence of stochastic forcing on a simple three-dimensional climate model previously derived by Saltzman and Sutera. A nonlinear dynamical system governing three physical variables, the bulk ocean temperature, continental and marine ice masses, is analyzed in deterministic and stochastic cases. It is shown that the attractor of deterministic model is either a stable equilibrium or a limit cycle. We demonstrate that the process of continental ice melting occurs with a noise-dependent time delay as compared with marine ice melting. The paleoclimate cyclicity which is near 100 ky in a wide range of model parameters abruptly increases in the vicinity of a bifurcation point and depends on the noise intensity. In a zone of stable equilibria, the 3D climate model under consideration is extremely excitable. Even for a weak random noise, the stochastic trajectories demonstrate a transition from small- to large-amplitude stochastic oscillations (SLASO). In a zone of stable cycles, SLASO transitions are analyzed too. We show that such stochastic transitions play an important role in the formation of a mixed-mode paleoclimate scenario. This mixed-mode dynamics with the intermittency of large- and small-amplitude stochastic oscillations and coherence resonance are investigated via analysis of interspike intervals. A tendency of dynamic paleoclimate to abrupt and rapid glaciations and deglaciations as well as its transition from order to chaos with increasing noise are shown.

      PubDate: 2016-12-04T02:03:09Z
      DOI: 10.1016/j.physd.2016.11.007
       
  • One- and two-dimensional bright solitons in inhomogeneous defocusing
           nonlinearities with an antisymmetric periodic gain and loss
    • Authors: Dengchu Guo; Jing Xiao; Linlin Gu; Hongzhen Jin; Liangwei Dong
      Abstract: Publication date: Available online 2 December 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Dengchu Guo, Jing Xiao, Linlin Gu, Hongzhen Jin, Liangwei Dong
      We address that various branches of bright solitons exist in a spatially inhomogeneous defocusing nonlinearity with an imprinted antisymmetric periodic gain-loss profile. The spectra of such systems with a purely imaginary potential never become complex and thus the parity-time symmetry is unbreakable. The mergence between pairs of soliton branches occurs at a critical gain-loss strength, above which no soliton solutions can be found. Intriguingly, which pair of soliton branches will merge together can be changed by varying the modulation frequency of gain and loss. Most branches of one-dimensional solitons are stable in wide parameter regions. We also provide the first example of two-dimensional bright solitons with unbreakable parity-time symmetry.

      PubDate: 2016-12-04T02:03:09Z
      DOI: 10.1016/j.physd.2016.11.005
       
  • A non-perturbative analytic expression of signal amplification factor in
           stochastic resonance
    • Authors: Asish Kumar Dhara
      Abstract: Publication date: Available online 21 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Asish Kumar Dhara
      We put forward a non-perturbative scheme to calculate the response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic force (signal) analytically. The formalism takes into account infinite number of perturbation terms of a perturbation series with amplitude of the signal as an expansion parameter. The contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in this formalism. A closed form analytic expression of the response is obtained. Only the knowledge of the first non-trivial eigenvalue and the lowest eigenfunction of the un-perturbed Fokker–Planck operator are needed to evaluate the response. The response calculated from the derived analytic expression matches fairly well with the numerical results.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.11.002
       
  • Optical dispersive shock waves in defocusing colloidal media
    • Authors: X. An; T.R. Marchant; N.F. Smyth
      Abstract: Publication date: Available online 24 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): X. An, T.R. Marchant, N.F. Smyth
      The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocussing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.11.004
       
  • Low-dimensional reduced-order models for statistical response and
           uncertainty quantification: Barotropic turbulence with topography
    • Authors: Di Qi; Andrew J. Majda
      Abstract: Publication date: Available online 25 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Di Qi, Andrew J. Majda
      A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty to changes in forcing in a barotropic turbulent system with topography involving interactions between small-scale motions and a large-scale mean flow. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model parameters. Statistical theories about a Gaussian invariant measure and the exact statistical energy equations are also developed for the truncated barotropic equations that can be used to improve the imperfect model prediction skill. A stringent paradigm model of 57 degrees of freedom is used to display the feasibility of the reduced-order methods. This simple model creates large-scale zonal mean flow shifting directions from westward to eastward jets with an abrupt change in amplitude when perturbations are applied, and prototype blocked and unblocked patterns can be generated in this simple model similar to the real natural system. Principal statistical responses in mean and variance can be captured by the reduced-order models with desirable accuracy and efficiency with only 3 resolved modes. An even more challenging regime with non-Gaussian equilibrium statistics using the fluctuation equations is also tested in the reduced-order models with accurate prediction using the first 5 resolved modes. These reduced-order models also show potential for uncertainty quantification and prediction in more complex realistic geophysical turbulent dynamical systems.

      PubDate: 2016-11-27T16:42:30Z
      DOI: 10.1016/j.physd.2016.11.006
       
  • Macroscopic heat transport equations and heat waves in nonequilibrium
           states
    • Authors: Yangyu Guo; David Jou; Moran Wang
      Abstract: Publication date: Available online 16 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Yangyu Guo, David Jou, Moran Wang
      Heat transport may behave as wave propagation when the time scale of processes decreases to be comparable to or smaller than the relaxation time of heat carriers. In this work, a generalized heat transport equation including nonlinear, nonlocal and relaxation terms is proposed, which sums up the Cattaneo-Vernotte, dual-phase-lag and phonon hydrodynamic models as special cases. In the frame of this equation, the heat wave propagations are investigated systematically in nonequilibrium steady states, which were usually studied around equilibrium states. The phase (or front) speed of heat waves is obtained through a perturbation solution to the heat differential equation, and found to be intimately related to the nonlinear and nonlocal terms. Thus, potential heat wave experiments in nonequilibrium states are devised to measure the coefficients in the generalized equation, which may throw light on understanding the physical mechanisms and macroscopic modeling of nanoscale heat transport.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.10.005
       
  • Spatiotemporal control to eliminate cardiac alternans using isostable
           reduction
    • Authors: Dan Wilson; Jeff Moehlis
      Abstract: Publication date: Available online 16 November 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Dan Wilson, Jeff Moehlis
      Cardiac alternans, an arrhythmia characterized by a beat-to-beat alternation of cardiac action potential durations, is widely believed to facilitate the transition from normal cardiac function to ventricular fibrillation and sudden cardiac death. Alternans arises due to an instability of a healthy period-1 rhythm, and most dynamical control strategies either require extensive knowledge of the cardiac system, making experimental validation difficult, or are model independent and sacrifice important information about the specific system under study. Isostable reduction provides an alternative approach, in which the response of a system to external perturbations can be used to reduce the complexity of a cardiac system, making it easier to work with from an analytical perspective while retaining many of its important features. Here, we use isostable reduction strategies to reduce the complexity of partial differential equation models of cardiac systems in order to develop energy optimal strategies for the elimination of alternans. Resulting control strategies require significantly less energy to terminate alternans than comparable strategies and do not require continuous state feedback.

      PubDate: 2016-11-20T14:57:33Z
      DOI: 10.1016/j.physd.2016.11.001
       
  • Finite-time thin film rupture driven by modified evaporative loss
    • Authors: Hangjie Ji; Thomas P. Witelski
      Abstract: Publication date: Available online 31 October 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Hangjie Ji, Thomas P. Witelski
      Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with modified evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term. Several different types of finite-time singularities are observed due to balances between conservative and non-conservative terms. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.

      PubDate: 2016-11-06T22:10:15Z
      DOI: 10.1016/j.physd.2016.10.002
       
  • Stability on time-dependent domains: Convective and dilution effects
    • Authors: R. Krechetnikov; E. Knobloch
      Abstract: Publication date: Available online 28 October 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): R. Krechetnikov, E. Knobloch
      In this paper we explore near-critical behavior of spatially extended systems on time-dependent spatial domains with convective and dilution effects due to domain flow. As a paradigm, we use the Swift-Hohenberg equation, which is the simplest nonlinear model with a finite non-zero critical wavenumber, to study dynamic pattern formation on time-dependent domains. A universal amplitude equation governing weakly nonlinear evolution of the pattern on time-dependent domains is derived and proves to be a generalization of the standard Ginzburg-Landau equation. Its key solutions identified here demonstrate a substantial variety–spatially periodic states with a time-dependent wavenumber, steady spatially non-periodic states, and pulse-train solutions–in contrast to extended systems on time-fixed domains. The effects of domain flow, such as bifurcation delay due to domain growth and destabilization due to oscillatory domain flow, on the Eckhaus instability responsible for phase slips of spatially periodic states are analyzed with the help of both local and global stability analyses. A nonlinear phase equation describing the approach to a phase-slip event is derived. Detailed analysis of a phase slip using multiple time scale methods demonstrates different mechanisms governing the wavelength changing process at different stages.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.10.003
       
  • Isolating blocks as computational tools in the circular restricted
           three-body problem
    • Authors: Rodney L. Anderson; Robert W. Easton; Martin W. Lo
      Abstract: Publication date: Available online 29 October 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Rodney L. Anderson, Robert W. Easton, Martin W. Lo
      Isolating blocks may be used as computational tools to search for the invariant manifolds of orbits and hyperbolic invariant sets associated with libration points while also giving additional insight into the dynamics of the flow in these regions. We use isolating blocks to investigate the dynamics of objects entering the Earth-Moon system in the circular restricted three-body problem with energies close to the energy of the L 2 libration point. Specifically, the stable and unstable manifolds of Lyapunov orbits and the hyperbolic invariant set around the libration points are obtained by numerically computing the way orbits exit from an isolating block in combination with a bisection method. Invariant spheres of solutions in the spatial problem may then be located using the resulting manifolds.

      PubDate: 2016-10-30T22:02:28Z
      DOI: 10.1016/j.physd.2016.10.004
       
  • Microorganism billiards
    • Authors: Saverio E. Spagnolie; Colin Wahl; Joseph Lukasik; Jean-Luc Thiffeault
      Abstract: Publication date: Available online 18 October 2016
      Source:Physica D: Nonlinear Phenomena
      Author(s): Saverio E. Spagnolie, Colin Wahl, Joseph Lukasik, Jean-Luc Thiffeault
      Recent experiments and numerical simulations have shown that certain types of microorganisms “reflect” off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of a body with this empirical reflection law inside a regular polygon and show that the dynamics can settle on a stable periodic orbit or can be chaotic, depending on the swimmer’s departure angle and the domain geometry. The dynamics are often found to be robust to the introduction of weak random fluctuations. The Lyapunov exponent of swimmer trajectories can be positive or negative, can have extremal values, and can have discontinuities depending on the degree of the polygon. A passive sorting device is proposed that traps swimmers of different departure angles into separate bins. We also study the external problem of a microorganism swimming in a patterned environment of square obstacles, where the departure angle dictates the possibility of trapping or diffusive trajectories.

      PubDate: 2016-10-23T18:28:43Z
      DOI: 10.1016/j.physd.2016.09.010
       
  • Modulational instability in a PT-symmetric vector nonlinear
           Schrödinger system
    • Authors: J.T. Cole; K.G. Makris Z.H. Musslimani D.N. Christodoulides Rotter
      Abstract: Publication date: 1 December 2016
      Source:Physica D: Nonlinear Phenomena, Volume 336
      Author(s): J.T. Cole, K.G. Makris, Z.H. Musslimani, D.N. Christodoulides, S. Rotter
      A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external P T -symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier–Floquet–Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet–Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

      PubDate: 2016-10-16T12:47:09Z
       
  • On loops in the hyperbolic locus of the complex Hénon map and their
           monodromies
    • Authors: Zin Arai
      Abstract: Publication date: 1 November 2016
      Source:Physica D: Nonlinear Phenomena, Volume 334
      Author(s): Zin Arai
      We prove John Hubbard’s conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex Hénon map. In fact, we show that there exist several non-trivial loops in the locus which generate infinitely many mutually different monodromies. Furthermore, we prove that the dynamics of the real Hénon map is completely determined by the monodromy of the complex Hénon map, providing the parameter of the map is contained in the hyperbolic horseshoe locus.

      PubDate: 2016-09-13T04:50:37Z
       
 
 
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
 
About JournalTOCs
API
Help
News (blog, publications)
JournalTOCs on Twitter   JournalTOCs on Facebook

JournalTOCs © 2009-2016